High-speed Imaging and Piv Measurements in Turbulent Cavitating Flows around 2d Hydrofoils

The paper reports on high-speed imaging and PIV study of cavitating flows around a flat plate with semicircular leading edge and a NACA0015 hydrofoil. Both foils were investigated at a series of attack angles ranging from 0 to 9° with varying cavitation number. Several known types of cavitation common to both foils, but also some different patterns, were registered. At small angles of incidence (less than 3°), cavitation on the plate begins in form of a streak array (bubble-band) whereas on the hydrofoil as travelling bubbles. For the regimes with developed cavitation on the NACA0015 hydrofoil, the scattered and discontinuous bubble streaks branch and grow but subsequently merge into bubble clouds forming a remarkably regular lattice pattern. Once the incidence angle increased to 9°, the cavitation on the hydrofoil changed to a streaky pattern like that on the plate at zero attack angle, whereas the regime on the plate showed no significant changes. The time-averaged velocity and turbulence moments show that the incipience of cavitation is governed by the development of the carrier-fluid flow around the foil leading edges, but the subsequent flow pattern depends strongly on the cavitation regime displaying markedly different distributions compared to the noncavitating case. The influence of the test object scale and the foil surface roughness on the cavitation pattern as well as on the mean velocity and turbulence intensity was analyzed. Thus, surface roughness leads to faster turbulization of the boundary layer and, consequently, to growth of the transversal dimension of the turbulent wake. Turbulent wake past the foil was shown to be wider for the larger hydrofoil due to the flow acceleration as a result of greater flow blockage. INTRODUCTION Flow in complex configurations of real power systems and their prime components – hydroturbines, supply ducts and draft tubes, are usually highly turbulent, unsteady and featured by large-scale vortical structures (LVS) and passive secondary motions of different origin and types. Often and especially at variable off-design loads, one unavoidably encounters cavitation and the consequent undesirable two-phase phenomena. The dispersed phase (bubbles, clouds) is governed by turbulence and the LSV dynamics (turbulent dispersion), while the bubble motion and the vapour-gas phase in general significantly changes properties of turbulent fluctuations in the carrier phase (turbulence modulation) due to a number of physical mechanisms. Nonlinear interactions of LSV with gasvapor dispersed phase lead often to strong flow pulsations, which may come into resonance with the structures natural frequency and cause excessive vibrations and, as a consequence, failure of hydraulic equipment or, at worst, even emergencies. The quest for improving the hydromachinery efficiency, durability and safety has necessitated ever-new studies of cavitation aimed at reducing its negative effects. More recently, these studies take the advantage of modern measuring techniques and computer simulations and are directed more towards gaining a deeper insight into physical mechanisms and processes, various regimes of cavitation and its interaction with flow of the carrier fluid. These methods make it possible to investigate simultaneously the spatial distribution and the time-dynamics of cavitationgenerated gas-vapour dispersed phase, the vortical and turbulence structures of the carrier fluid and their interactions. This, in turn, should lead to better understanding August 28 30, 2013 Poitiers, France MULB 2 and the ability to forecast cavitation and the consequent erosion, as well as to provide guidance for their control. It is noted, however, that the methods for reducing the negative effects of cavitation have to satisfy the requirement for power loss minimization. Despite extensive research, detailed quantitative information for cavitating flows required for design and optimization, as well as for verification of the existing and development of advanced mathematical models, is still lacking and, to a large extent, limited to simplified conditions and usually 2D geometries. Experiments on fullscale objects are very difficult or can even be impossible, but the laboratory investigations are also costly and require expensive laboratory setups. Thus, most publications in the literature report on research in simple geometries (Venturi nozzles, scaled-down shaped bodies, e.g. NACA series hydrofoils, etc.) though at varying conditions and with focus on diverse issues of the cavitation incipience and development of different regimes. The acquisition of systematic experimental data for various cavitation regimes is still an issue. Depending on flow conditions (foil shape and surface texture, velocity and pressure fields, overall flow configuration and others), one can distinguish a variety of cavitation patterns (bubbles, vortex or cloud cavitation, supercavitation, etc.), but practically all spatial cavitation patterns can be grouped into two generic types – partial cavities and supercavities. Partial cavities occur when a cavity closes on the cavitating surface, while a supercavity closes downstream in the wake of the cavitating object. The partial cavities can further be classified into closed and open cavities, depending on the flow in the cavity closure region (Laberteaux and Ceccio, 2001). A typical example of closed cavities is the sheet cavitation whereas that of the open cavities is the cloud cavitation. A cloud cavitation arises when a large portion of vapour-filled cavity underlined with re-entrant fluid breaks off, forming a cavitation cloud. Experimental studies report on visual observations and regime maps with qualitative descriptions (e.g. Franc and Michel, 1985), point pressure measurements (Cervone et al., 2006) and, sometimes, velocity distributions (Kubota et al., 1989). Measurements of the local volume fraction of vapor phase within a cavity and in the wake past a foil were also reported (e.g. Coutier-Delgosha et al., 2006). The impact of thermal effects on the onset of various forms of cavitation and instabilities was studied by Cervone et al. (2006), etc. Much of the works published in the literature deal with the experimental investigation of cloud cavitation (e.g. Kawanami et al., 1997 and Callenaere et al., 2001). As widely acknowledged, when a sheet cavity reaches a certain dimension, periodic oscillations of cavity appear. This process is accompanied by a cavity (in the form of clouds) shedding downstream. Kubota et al. (1989) showed that a cloud cavity consists of a large-scale vortex and a cluster of small vapor bubbles situated in the core of the vortex. In various experiments (e.g. George et al., 2000), it was revealed that cloud cavity pulsations occur at similar Strouhal numbers. Callenaere et al. (2001) proposed correlations between separation of a cloud cavity and the re-entrant jet generated in the cavity closure region due to the adverse pressure gradient. The present paper aims at investigating the mutual impact of the flow hydrodynamics and a partial cavity initiation and detachment, as well as cloud cavity shedding on 2D hydrofoils. It also reports on the results of highspeed imaging of the cavitating foils and the PIVmeasurements of spatial distributions of mean and turbulent characteristics about the foils at various flow conditions. Besides, the scale effect and test object roughness impact on the cavitation inception, cavity development and turbulence intensity distribution are of a special interest in the present work. EXPERIMENTAL CONDITIONS AND MEASUREMENT TECHNIQUE Experiments were carried out in the Cavitation tunnel of the Institute of Thermophysics SB RAS. Detailed description of the setup can be found in Kravtsova et al. (2012). We investigated the spatial structure and dynamics of partial cavities and measured the velocity and turbulence intensity in flows around a 2D plate with semi-cylindrical nose and sharp-cut end (100 mm chord and 15 mm thickness), and a NACA0015 series hydrofoil (100 mm chord) at four attack angles α = 0, 3, 6 and 9°. The test objects were made of brass with roughness level of about 2.8 μm. In order to investigate the impact of roughness on the onset of cavitation and partial cavities development we utilized one more NACA0015 hydrofoil with roughness level of 4.5 μm as a test object. The scale effect on the cavities and turbulence intensity was studied on three NACA0015 foils with chord lengths of 50, 100 and 200 mm. The working liquid was distilled water. The amount of dissolved air in liquid was estimated by Henry’s law under the normal conditions to be approximately 0.023 g of air in 1 kg of water. The liquid temperature was kept at 30°C with uncertainty of ±0.1°C and the overpressure in the setup was fixed to 0.5 bars. The flow regime is defined by the cavitation number, σ = (Pin – PV)/(ρU0 /2), where Pin is the static pressure at the test section inlet, PV is the water vapour pressure, U0 is the bulk flow velocity. In order to observe various cavity patterns, the cavitation number was adjusted by varying the dynamic pressure, ρU0 /2, in the range from 0.5 to 5.5. Under the present conditions, PV = 0.044 bar. The initial turbulence intensity was lower than 1%. The Reynolds number, Re, based on U0 and the chord length, C, was in the range between 0.8×10 and 1.7×10. The Strouhal number, St, for the nondimensional cloud shedding frequency is defined in terms of the cloud streamwise dimension Dcl and the cloud convection velocity Ucl. The uncertainties in defining of cavitation number and estimating the Reynolds and Strouhal numbers were 6%, 3% and 4%, respectively. The dynamics and spatial structure of gas-vapor cavities was analysed by high-speed visualization using Photron FASTCAM SA5 camera at a frame rate of 20-100 kHz taken from above and from the side. The velocity fields were measured by a “PIV-IT” PIV-system consisting of a double-pulsed Nd:YAG Quantel EVG00200 laser (wavelength 532 nm, repetition rate 15 Hz, pulse duration 10 ns, pulse energy 200 mJ), a CCD-camera (10 bits per pixel, matrix resolution 2048×2048 pixels) equipped with Nikon AF Nikkor 50 mm f/1.4D lens and an optical lowpass filter (bandpass edge at 570 nm), as well as a synchronizing processor. The PIV-system was operated via a computer using "ActualFlow" software (Akhmetbekov et al., 2006). The thickness of the laser light sheet formed by a cylindrical lens to illuminate tracer particles was about 0.8 mm in the measurement plane that coincided with the central longitudinal plane of the test section parallel to its larger sidewalls. The distance between the camera and the August 28 30, 2013 Poitiers, France MULB 3 laser sheet was 527 mm. The size of the measurement area was approximately 124×124 mm. Since in a cavitating flow the micro-size vapour bubbles can act as tracers, their contaminating effect on the PIV measurements was reduced by adding fluorescent tracers (average size 10 μm, wavelength range 550-700 nm) into the working liquid. RESULTS The results of the visualization and field measurements (velocity and turbulence statistics) are given only for α = 3° because of the limitations of the Conference paper format. This value of the attack angle was selected as the most illustrative both for the qualitative and quantitative descriptions of characteristic features of cavitating flows. In all plots, the reference point coincides with the leading edge of a foil in the measurement plane at α = 0°. Visualization Fig. 1 shows typical patterns of partial cavities occurring on the suction side of the plate and NACA0015 foil. In the case of plate, cavitation inception occurs at σ ≈ 2.78 as a bubble-band – an array of bubble-filled streamwise streaks – which differ from the common sheet attached cavity found sometimes behind the leading edge of the foil. Similar streaks were registered by Brandner et al. (2010). The cavity length is LC/C = 0.07. The typical distance between the streaks is about 1 mm. This cavitation pattern persists until approximately σ = 2.26 (Fig. 1). As the cavitation number is decreased, the streaks become thicker and tend to interact and merge, forming what now may be qualified as an attached streaky-sheet cavity. Here it should be noted that the cavity interface is frothy and, in contrast to results of other papers in the literature (e.g. Franc and Michel, 1985), in the present work the sheet cavity is accompanied by shedding of small (up to 0.02C) clusters of bubbles at the cavity closure region. This is suspected to be due to either a relatively high level of roughness of the hydrofoil surface or a relatively large (compared to deaerated water) amount of dissolved air in the water. As well known, a decrease of the cavitation number leads to the growth of the streamwise extent of the cavity and even to transition to another cavity pattern when a certain threshold is overcome. When the cavitation number is decreased to σ = 1.7 (Fig. 1), the cavity changes to be of transitional type. At this regime, the spatial structure of the cavity is essentially 3D. The cavity length increases up to LC/C = 0.23. Downstream, an increase in local pressure leads to the collapse of micro-bubbles and, consequently, a drop of dispersed-phase concentration. A further decrease of cavitation number results in cloud cavitation (Fig. 1). It is proved that separation of cloud 1 Sheet cavity represents a gas-vapor film of a relatively stable length with clear interface. In the region of the sheet cavity closure, the main flow reattaches to the solid surface of the cavitating object. 2 This cavity type is intermediate between sheet and cloud cavities. In general, at the closure region transitional cavity is accompanied by continuous shedding of relatively small clouds and larger horseshoe-shaped ones consisting of a bulk of gas-vapor micro-bubbles at different parts of the cavity closure region. 3 As widely acknowledged, cloud cavities are characterized by detachment of the whole cavity from foil surface and quasicavity is accompanied by liquid circulation, which leads to formation of a large-scale vortex around the cloud cavity (Kubota et al., 1989). The characteristic Strouhal numbers for the cloud cavitation regimes are given in the caption of Fig. 1. When σ = 1.14, the cavity extent grows up to LC/C = 1.1 and the size of detached clouds rises as well. Figure 1. Instantaneous images of partial cavities (top view) on the suction side of the plate (the upper row) and the NACA0015 hydrofoil (the lower row) at α = 3°. In addition, downstream of the plate, one can observe thin streamwise and spanwise structures filled up with vapor and gas. Their origin seems to be connected with generation of strong vortices past the trailing edge of the plate. Inside the cores of those vortices, local pressure most probably falls below the vapor pressure, leading to water vaporization. In the case of NACA0015 hydrofoil, flow pattern differs significantly. Initially, when σ = 1.14 separate microbubbles arise at a distance of about 0.03C downstream from the leading edge of the hydrofoil (Fig. 1). These bubbles are convected downstream with the local fluid velocity of 17.1 m/s. The bubble size grows at a rate of about 5.8 m/s. Such dynamics of bubble growth and movement can be observed until the bubbles collapse further downstream. As suspected, at this threshold location the magnitude of the local pressure reaches the value that periodic cloud shedding process due to the appearance of reentrant jet. A detailed description of cloud cavitation can be found e.g. in Callenaere et al. (2001). flow direction 3 α = ° x z flow direction 2.26 =0.07 C L C σ = 1.70 =0.23 C L C σ = 1.38 =0.50 St = 0.43 C L C σ = 1.14 =1.10 St = 0.13 C L C σ = 1.14 σ = 1.06 =0.54 C L C σ = 0.93 =0.66 St 0.14 C L C σ = = 0.90 =1.06 St = 0.07 C L C σ = leading edge ------------------------trailing edge ------------------------leading edge ------------------------trailing edge ------------------------collapse curve flow direction 3 α = ° x z flow direction August 28 30, 2013 Poitiers, France MULB 4 is sufficient to cause the bubble collapse. This cavitation pattern is referred to as the traveling bubble cavitation. At this regime, the cavity is not formed yet. When the cavitation number becomes lower (Fig. 1), a transitional cavity type can be observed. As in the previous case, the micro-bubbles initiate from the leading edge of the cavity and extend roughly to the hydrofoil halflength. The bubble size varies from zero up to 0.13C. It should be noted that the cavity leading edge is quite difficult to determine. The trailing part of the cavity is frothy. At the cavity closure region, the bubbles collapse and separate into horseshoe-shaped clouds immediately downstream. These clouds are likely to be situated in the vortex cores and replicate their forms. When σ is about 0.9 (Fig. 1), cloud cavitation occurs. However, as in the case with transitional cavity, one can observe horseshoe-shaped clouds together with the large-scale ones. Turbulent characteristics Based on the ensemble of 5000 instantaneous velocity fields in the vertical midplane, the distributions of the mean velocity, turbulent kinetic energy, secondand thirdorder statistical moments of turbulent fluctuations were calculated over the suction side of the two foils considered. Fig. 2 shows some profiles of the streamwise component of the mean velocity excess over the bulk flow velocity, (U – U0)/U0, with superimposed isocontours for both foils at the attack angle α = 3° for three different types of cavitation. In the front of the leading edge (not shown here), the flow locally decelerates approaching the stagnation point and the region of slowdown shifts to the pressure side of the foils in all the cases. The mean velocity profiles at x/C = 0 are almost identical for all the regimes. Due to the flow deflection and acceleration around the leading edge, the mean velocity reaches soon its maximum above the upper surface of the foils. When σ decreases, the velocity maximum firstly increases and moves downstream but then gradually decreases and shifts upstream. In the case of plate, the reverse shift of the maximum along x-axis, noticed on the hydrofoil, does not occur. The above findings can be explained in the following way. Unsteady cavity is characterized by pulsations of its closure. Consequently, pulsations at the cavity trailing edge lead to an increase in liquid velocity fluctuations (Fig. 3), more intensive mixing and lateral momentum transfer, which, in turn, reduce the velocity peaks. Downstream from the region of higher mean velocity along the suction side of the hydrofoils, the mean velocity peaks decrease and eventually disappear, except for the plate at the higher cavitation number (Fig. 2) where at the plate end, x/C = 1.0, mild velocity peaks appear again due to the vanishing wall shear at the edge separation. No separation on any of the foils has been detected apart from the trailing edge of the plate. In the case of plate, the transverse dimension of the wake is significantly larger owing to its bluff shape and reaches 0.23C. This is caused by generation of large-scale vortex structures in the shear layers over the cloud cavity. Here it should be noted that these observations are only for the averaged properties, as the separation points (lines) are not fixed but pulsate around a mean value. No doubt, hydrodynamic flow separation and the cavitation cloud detachment are interlinked and mutually dependent, but at this stage, it is difficult to portray a clear scenario of this nonlinear interaction. For incipient and mild cavitation, flow separation can be considered as being fully controlled by the hydrodynamics of the carrier fluid, i.e. the adverse pressure gradient on the trailing part of the foil. However, cavitation is always followed by expansion of the gas-vapor phase and the consequent flow acceleration, which will tend to delay flow separation. On the other hand, detachment of cavity clouds have been observed in non-separating flows, though in most cases it is accompanied with re-entrant jet flow underneath, which is indicative of flow separation. It seems plausible, however, that cloud detachment will trigger and promote flow separation and affect its behavior. Plate with rounded nose NACA0015 hydrofoil